Cosmological Scales, the Universe as a Hologram

Here we deduce the scales of a spherically symmetric, closed system subject to internal repulsive vacuum pressure. Due to periodic boundary conditions of virtual particle loops, it is shown that Ramanujan summation must be physical for the virtual particle case, as to avoid numerical results of either null, very large or infinity. It is thereafter shown that this closed system must be holographic in nature, with mass-energy inversely proportional to the Planck area, up to a yet to be determined geometrical proportionality constant. The validity of this result is strengthened when it is shown that one may obtain the same answer using different methods, either thermodynamic laws or a force balance equation. Implications of this small study is not yet fully understood and is hopefully investigated in subsequent letters.